Question 148
Points $A$ and $B$ lie on circle $\omega$ with center $O$. Let $X$ be a point inside $\omega$. Suppose that $XO = 2\sqrt{2}$, $XA = 1$, $XB = 3$, and $\angle AXB = 90^{\circ}$. Points $Y$ and $Z$ are on $\omega$ such that $Y \neq A$ and triangles $\triangle AXB$ and $\triangle YXZ$ are similar with the same orientation. Compute $XY$.